Geometry from the spectral point of view
- 279 Downloads
In this Letter, we develop geometry from a spectral point of view, the geometric data being encoded by a triple (A. H. D.) of an algebraA represented in a Hilbert spaceH with selfadjoint operatorD. This point of view is dictated by the general framework of noncommutative geometry and allows us to use geometric ideas in many situations beyond Riemannian geometry.
Mathematics Subject Classifications (1991)46L60 46L80 46L87 19K56 58H15 58A12
Unable to display preview. Download preview PDF.
- 2.Connes, A.: Cyclic cohomology and the transverse fundamental class of a foliation, inGeometric Methods in Operator Algebras (Kyoto, 1983), Pitman Res. Notes in Math. 123 Longman, Harlow, 1986, pp. 52–144.Google Scholar
- 3.Connes, A.: Noncommutative geometry and physics, Les Houches, Preprint IHES M/93/32. 1993.Google Scholar
- 4.Connes, A. and Lott, J.: Particle models and noncommutative geometry,Nuclear Phys. B 18 (1990), suppl. 29–47 (1991).Google Scholar
- 6.Connes, A. and Moscovici, H.: The local index formula in noncommutative geometry. To appear inGAFA.Google Scholar